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Journal articles on the topic 'Structural stability Mathematical models'
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1
Kostrobij, P. P., and I. A. Ryzha. "Stability of carbon monoxide oxidation process on gold nanoparticles." Mathematical Modeling and Computing 8, no. 1 (2020): 116–24. http://dx.doi.org/10.23939/mmc2021.01.116.
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The stability conditions for mathematical models of carbon monoxide oxidation on the surface of gold nanoparticles are investigated. The cases of reaction mechanisms of one-step and step-by-step transformation of reagents are consecutively considered. Using the stability analysis by Lyapunov method, it is shown that models which take into account the possibility of structural changes of the catalyst surface can predict the occurrence of oscillatory mode in the system as a result of Hopf instability.
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Smirnov, Sergey N. "Realistic Models of Financial Market and Structural Stability." Journal of Mathematics 2021 (June 21, 2021): 1–8. http://dx.doi.org/10.1155/2021/6651324.
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The main aim of this article is to show the role of structural stability in financial modelling; that is, a specific “no-arbitrage” property is unaffected by small perturbations of the model’s dynamics. We prove that under the structural stability assumption, given a convex compact-valued multifunction, there exists a stochastic transition kernel with supports coinciding with this multifunction and one that is strong Feller in the strict sense. We also demonstrate preservation of structural stability for sufficiently small deviations of transition kernels for different probability metrics.
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DUCROT, ARNAUD. "STRUCTURAL STABILITY OF COMBUSTION MODELS WITH COMPLEX CHEMISTRY." Mathematical Models and Methods in Applied Sciences 16, no. 06 (June 2006): 793–817. http://dx.doi.org/10.1142/s0218202506001352.
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This work is devoted to the study of semi-linear elliptic systems in unbounded cylinders with linear dependence of the components of the nonlinearity vector. We reduce the study of such a problem with non-Fredholm operator to the study of a perturbation of some reaction-diffusion operator which satisfies the Fredholm property. Then sufficient conditions that ensure the structural stability of particular solutions are given. These conditions are applied to derive some existence results for some combustion model with complex chemistry and for some KPP like system.
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Kulik, Anatoliy, Konstantin Dergachov, Sergey Pasichnik, and Sergey Yashyn. "Motions models of a two-wheeled experimental sample." RADIOELECTRONIC AND COMPUTER SYSTEMS, no. 1 (February 27, 2021): 40–49. http://dx.doi.org/10.32620/reks.2021.1.03.
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The subject of study is the physical processes of translational and angular motion of a two-wheeled experimental sample. The goal is to develop physical, mathematical, and graphic models of the translational and angular motions of a two-wheeled experimental sample as an object of automatic control. The objectives: to form physical models of a two-wheeled experimental sample; to develop a nonlinear mathematical description of the processes of translational and angular sample`s motions using the Lagrange approach; to obtain a linearized mathematical sample`s description as an object of automatic control in the state space and frequency domain; to generate graphic models in the form of structural diagrams in the time and frequency domains; to analyze the functional properties of an object of automatic control: stability, controllability, observability, structural and signal diagnosability concerning violations of the functional properties of electric drives and sensors of the angular position of the body and wheels. The methods of the study: the Lagrange method, Taylor series, state-space method, Laplace transformations, Lyapunov, Kalman criteria, and diagnosability criterion. The results: physical models of a two-wheeled experimental sample have been obtained in the form of a kinematic diagram of the mechanical part and the electric circuit of an electric drive; mathematical descriptions of translational and angular motions have been developed in nonlinear and linearized forms; structural diagrams have been developed; functional characteristics of a two-wheeled experimental model as an object of automatic control have been analyzed to solve problems of control algorithms synthesis. Conclusions. The scientific novelty lies in obtaining new models that describe the translational and angular motion of a two-wheeled experimental model as an object of automatic control. The obtained models differ from the known ones by considering the dynamic properties of sensors and electric drives, as well as the relationship of movements.
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Nguyen, Ngoc Hung, Van Phan Do, and Hoa Tien Vu. "Estimating Disturbance Torque Effects on the Stability and Control Performance of Two-Axis Gimbal Systems." Journal of the Russian Universities. Radioelectronics 25, no. 4 (September 29, 2022): 63–71. http://dx.doi.org/10.32603/1993-8985-2022-25-4-63-71.
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Introduction. Two-axis gimbal systems are applied for stabilizing and controlling the line of sight (LOS) of an optical or imaging system mounted on a moving vehicle. Gimbal systems are intended to isolate various disturbance torques and control the LOS toward the direction of a target. Two-axis gimbals can be of two main types, namely Yaw-Pitch and Swing-Roll type. In this article, we focus on investigating mathematical models of two-axis gimbals, which describe the impact of cross-disturbance torques on their stability and control performance. Simulations were conducted to compare advantages and disadvantages of the two types of two-axis gimbals.Aim. To study mathematical models describing the impact of cross-disturbance torques on the stability and control performance of two-axis gimbals.Materials and methods. Mathematical models of two-axis gimbal systems were synthesized by the Lagrange method. The operation of two-axis gimbal systems was simulated in the Matlab-Simulink environment. Results. Mathematical models and structural diagrams of the synthesized Yaw-Pitch and Swing-Roll gimbals were obtained. The conducted simulations of typical cases revealed different cross-disturbance effects.Conclusion. Motion equations for Swing-Roll and Yaw-Pitch gimbals were derived using similar methodology. The impact of cross-disturbance torques on gimbal systems was evaluated. The obtained results form a basis for selecting an optimal structure of tracking systems meeting the desired characteristics.
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WYLLER, JOHN, PATRICK BLOMQUIST, and GAUTE T. EINEVOLL. "ON THE ORIGIN AND PROPERTIES OF TWO-POPULATION NEURAL FIELD MODELS - A TUTORIAL INTRODUCTION." Biophysical Reviews and Letters 02, no. 01 (January 2007): 79–98. http://dx.doi.org/10.1142/s1793048007000441.
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Neural field models have a long tradition in mathematical neuroscience, and in the present tutorial paper we outline the neurobiological and biophysical origin of such models, in particular two-population field models describing excitatory and inhibitory neurons interacting via nonlocal spatial connections. Results from investigations of such models on the existence and stability of stationary localized activity pulses ('bumps') and generation of stationary spatial and spatiotemporal oscillations through Turing-type instabilities are described.
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Corradi, Valentina, and Norman R. Swanson. "Testing for structural stability of factor augmented forecasting models." Journal of Econometrics 182, no. 1 (September 2014): 100–118. http://dx.doi.org/10.1016/j.jeconom.2014.04.011.
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Maldhure, Atul V., and Jayant D. Ekhe. "Effect of modifications of lignin on thermal, structural, and mechanical properties of polypropylene/modified lignin blends." Journal of Thermoplastic Composite Materials 30, no. 5 (October 22, 2015): 625–45. http://dx.doi.org/10.1177/0892705715610402.
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Use of organic biomass, industrial waste lignin, was considered interesting due to its easy availability, polymeric nature, and ample scope to modify with an aim to replace conventional metal oxides to achieve improved properties of the blend when blended with polyolefins. To study the effect of chemical modification of lignin on the thermal, structural, and mechanical properties of polypropylene (PP)/modified lignin blends, purified industrial waste lignin was modified by two different chemical methods and blended in various proportions in PP matrix. The thermal stability of the blends was studied by thermogravimetric analysis, whereas melting and crystallization behavior of blends was studied by non-isothermal differential scanning calorimetry. The results show improved thermal stability of blends with increasing modified lignin proportion in the PP matrix. More depression in melting point was observed in PP/alkylated lignin blends than PP/arylated lignin blends, whereas addition of alkylated lignin shows polymorphism in PP matrix. Intermolecular interactions between blend components have been evaluated by applying several mathematical models to experimental mechanical property data. In most of the cases, good agreement has been obtained between the predictions made by using mathematical models and interpretations done on the basis of experimental data, showing the suitability of these models for predicting the mechanical properties of PP/modified lignin blends.
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Barigozzi, Matteo, and Lorenzo Trapani. "Sequential testing for structural stability in approximate factor models." Stochastic Processes and their Applications 130, no. 8 (August 2020): 5149–87. http://dx.doi.org/10.1016/j.spa.2020.03.003.
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Akimov, Pavel A., Alexandr M. Belostosky, Marina L. Mozgaleva, Mojtaba Aslami, and Oleg A. Negrozov. "Correct Multilevel Discrete-Continual Finite Element Method of Structural Analysis." Advanced Materials Research 1040 (September 2014): 664–69. http://dx.doi.org/10.4028/www.scientific.net/amr.1040.664.
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The distinctive paper is devoted to correct multilevel discrete-continual finite element method (DCFEM) of structural analysis based on precise analytical solutions of resulting multipoint boundary problems for systems of ordinary differential equations with piecewise-constant coefficients. Corresponding semianalytical (discrete-continual) formulations are contemporary mathematical models which currently becoming available for computer realization. Major peculiarities of DCFEM include universality, computer-oriented algorithm involving theory of distributions, computational stability, optimal conditionality of resulting systems and partial Jordan decompositions of matrices of coefficients, eliminating necessity of calculation of root vectors.
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Balint, Stefan, Agneta Maria Balint, and Achim Ionita. "Oscillation Susceptibility Analysis of the ADMIRE Aircraft along the Path of Longitudinal Flight Equilibriums in Two Different Mathematical Models." Differential Equations and Nonlinear Mechanics 2009 (2009): 1–26. http://dx.doi.org/10.1155/2009/842656.
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The oscillation susceptibility of the ADMIRE aircraft along the path of longitudinal flight equilibriums is analyzed numerically in the general and in a simplified flight model. More precisely, the longitudinal flight equilibriums, the stability of these equilibriums, and the existence of bifurcations along the path of these equilibriums are researched in both models. Maneuvers and appropriate piloting tasks for the touch-down moment are simulated in both models. The computed results obtained in the models are compared in order to see if the movement concerning the landing phase computed in the simplified model is similar to that computed in the general model. The similarity we find is not a proof of the structural stability of the simplified system, what as far we know never been made, but can increase the confidence that the simplified system correctly describes the real phenomenon.
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Lei, Mingfeng, Linghui Liu, Yuexiang Lin, Chenghua Shi, Weichao Yang, Chengyong Cao, and Yao Liu. "Research Progress on Stability of Slurry Wall Trench of Underground Diaphragm Wall and Design Method of Slurry Unit Weight." Advances in Civil Engineering 2019 (December 16, 2019): 1–19. http://dx.doi.org/10.1155/2019/3965374.
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This paper performs an extensive literature survey and example investigation on the stabilisation of slurry wall trenches during the construction of diaphragm wall panel trenches, and the failure modes of slurry wall trench instability, the stability theoretical analysis models and methods, the slurry formation and its protection mechanism, the influence of related factors on slurry wall trench stabilisation, and other related problems are summarized and analyzed emphatically. And then, based on the limit equilibrium analysis method, the mechanical models of the overall stability and local stability of the trench wall are established, respectively, and the design method of slurry unit weight is derived to ensure the stability of the trench wall. Furthermore, an example application shows that the established slurry unit weight design method is reliable. At last, this paper also proposes the focus and direction for follow-up work, that is, to construct an accurate and effective theoretical analysis model of slurry wall trench instability considering the influence of multiple factors and the calculation method of the slurry cake and its mechanical or mathematical relationship with slurry quality.
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Xu, Min, Lin Zhu, and Ze Xiang Cai. "The Unified Design for Inter-Area Stability Control Based on Backstepping." Advanced Materials Research 383-390 (November 2011): 1124–30. http://dx.doi.org/10.4028/www.scientific.net/amr.383-390.1124.
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This paper proposes a unified method for inter-area power oscillations which is the key to solve coordination problems caused by different mathematical models and control theories. Firstly, the unified model, breaking the constraints of the network topology, component and the precise extents in the process, is established based on global signals. Secondly, making use of the structural feature of the unified system model, it combines advanced control theory to resolve the problem of parameter uncertainty and model error. Finally, the control law is effectively derived with backstepping method. The simulation results in Matlab show the validity of the proposed method.
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Wei, Yi, Shuilong He, Enyong Xu, Genge Zhang, Rongjiang Tang, Wei Wang, and Chao Li. "Steady-State Steering Characteristics of Mathematical Model for Semitrailer Based on Variations in Camber Parameters." Shock and Vibration 2020 (June 13, 2020): 1–14. http://dx.doi.org/10.1155/2020/6272397.
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To master the basic characteristics of steady-state cornering for a semitrailer, this paper summarises the current modelling methods for handling and stability and discusses their limitations. The classical linear mathematical model for a two-degree-of-freedom (DOF) handling and stability system is used to develop a new model. Analysis methods are proposed to introduce the influence of the camber angle and body roll into the model parameters. Thus, a mathematical model for the lateral stability of semitrailer with five DOFs is established. At the same time, a modified formula to calculate the stability factor of the semitrailer is developed with a MATLAB model to solve the dynamic state equation. The mathematical model, which considers the body roll and the changes in the camber angle caused by roll, compares the turning radius ratio and yaw rate as the evaluation index with the classical linear mathematical model of a two-DOF system. The vehicle parameters for three different types of semi-tractor trailers are used to calculate and compare two mathematical models for handling and stability using real vehicle test data. The results show that the new modelling and analysis method proposed in this paper has a high calculation accuracy and fast calculation speed, is clear and concise, and is consistent with the real vehicle test data. In addition, the accuracy of the new mathematical model for handling and stability and the improved stability factor are verified.
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Ahmed, N. U., and H. Harbi. "Stability of suspension bridge I: Aerodynamic and structural damping." Mathematical Problems in Engineering 4, no. 1 (1998): 73–98. http://dx.doi.org/10.1155/s1024123x98000738.
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In this paper we consider a few dynamic models of suspension bridge described by partial differential equations with linear and nonlinear couplings. We study analytically the stability properties of these models and the relative effectiveness of aerodynamic and structural damping. Increasing aerodynamic or structural damping indefinitely does not necessarily increase the decay rate indefinitely. In view of possible disastrous effects of high wind, structural damping is preferable to aerodynamic (viscous) damping. These results are illustrated by numerical simulation.
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Harfash, Akil J. "Structural Stability for Two Convection Models in a Reacting Fluid with Magnetic Field Effect." Annales Henri Poincaré 15, no. 12 (December 18, 2013): 2441–65. http://dx.doi.org/10.1007/s00023-013-0307-z.
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Yue, Jing Tao, Hui Pu, and Xiao Jun Wei. "The Transitional Simulation of Self-Propelled Winch System by the AMESim." Applied Mechanics and Materials 687-691 (November 2014): 228–31. http://dx.doi.org/10.4028/www.scientific.net/amm.687-691.228.
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The self-propelled winch system was studied taking the 20-ton transitional self-driven winch system as the engineering background. By the analysis of structural characteristics, control loops, speed solutions and hydraulic motor-driven forms of winch hydraulic system, The system of mathematical models was established which lay the foundation of the establishment of system simulation model. The walking hydraulic drive system simulation models were established by using AMESim software. On this basis, by setting different parameters, the simulation system operating conditions are simulated, which verified the rationality and stability of the design of the winch hydraulic transmission system.
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Dimitriadis, G., and J. E. Cooper. "A method for identification of non-linear multi-degree-of-freedom systems." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 212, no. 4 (April 1, 1998): 287–98. http://dx.doi.org/10.1243/0954410981532441.
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System identification methods for non-linear aeroelastic systems could find uses in many aeroelastic applications such as validating finite element models and tracking the stability of aircraft during flight flutter testing. The effectiveness of existing non-linear system identification techniques is limited by various factors such as the complexity of the system under investigation and the type of non-linearities present. In this work, a new approach is introduced which can identify multi-degree-of-freedom systems featuring any type of non-linear function, including discontinuous functions. The method is shown to yield accurate identification of three mathematical models of aeroelastic systems containing a wide range of structural non-linearities.
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MEIMAND, VAHID ZEINODDINI, LORI GRAHAM-BRADY, and BENJAMIN WILLIAM SCHAFER. "IMPERFECTION SENSITIVITY AND RELIABILITY USING SIMPLE BAR-SPRING MODELS FOR STABILITY." International Journal of Structural Stability and Dynamics 13, no. 03 (April 2013): 1250075. http://dx.doi.org/10.1142/s0219455412500757.
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The objective of this paper is to demonstrate how simple bar-spring models can illustrate elementary and advanced structural behavior, including stability, imperfection sensitivity, and plastic collapse. In addition, the same bar-spring models also provide a ready means for assessing structural reliability. Bar-spring models for a column (both post-buckling stable and unstable), a frame, and a plate are all developed. For each model the influence of geometric imperfections are explicitly introduced and the ultimate strength considering plastic collapse of the supporting springs derived. The developed expressions are compared to material and geometric nonlinear finite element analysis models of analogous continuous systems, using yield surface based plastic hinge beam elements (in MASTAN) for the column and frame and shell elements (in ABAQUS) for the plate. The results show excellent qualitative agreement, and surprisingly good quantitative agreement. The developed bar-spring models are used in Monte Carlo simulations and in the development of first order Taylor Series approximations to provide the statistics of the ultimate strength as used in structural reliability calculations. Good agreement between conventional first order second moment assumptions and the Monte Carlo simulations of the bar-spring models is demonstrated. It is intended that the developed models provide a useful illustration of basic concepts central to structural stability and structural reliability.
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LAZKOZ, RUTH. "RIGIDITY OF COSMIC ACCELERATION IN A CLASS OF k-ESSENCE COSMOLOGIES." International Journal of Modern Physics D 14, no. 03n04 (April 2005): 635–41. http://dx.doi.org/10.1142/s0218271805006560.
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We study the structural stability of a cosmic acceleration (inflation) in a class of k-essence cosmologies against changes in the shape of the potential. Those models may be viewed as generalized tachyon cosmologies and this analysis extends previous results on the structural stability of cosmic acceleration in tachyon cosmologies. The study considers both phantom and non-phantom cases. The concepts of rigidity and fragility are defined through a condition on the functional form of the Hubble factor. Given the known result of the existence of inflationary (non-phantom) and super-inflationary (phantom) attractors we formulate the question of their structural stability. We find that those attractors are rigid in the sense that they never change as long as the conditions for inflation or super-inflation are met.
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Avila-Becerril, Sofía, Gerardo Espinosa-Pérez, and Paul Fernandez. "Dynamic Characterization of Typical Electrical Circuits via Structural Properties." Mathematical Problems in Engineering 2016 (2016): 1–13. http://dx.doi.org/10.1155/2016/7870462.
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The characterization of a class of electrical circuits is carried out in terms of both stability properties and steady-state behavior. The main contribution is the interpretation of the electrical topology (how the elements that conform the circuits are interconnected) in terms of mathematical properties derived from the structure of their models. In this sense, at what extent the topology by itself defines the dynamic behavior of the systems is explained. The study is based on the graph theory allowing capturing, departing from the well-known Kirchhoff laws, the topology of the circuits into several matrices with specific structure. The algebraic analysis of these matrices permits identifying conditions that determine whether the system is stable in the sense of Lyapunov and the kind of steady-state behavior that it exhibits. The approach is mainly focused on typical topologies widely used in practice, namely, radial, ring, and mesh networks.
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Zumatov, S. S. "On a program manifold’s stability of one contour automatic control systems." Open Engineering 7, no. 1 (December 29, 2017): 479–84. http://dx.doi.org/10.1515/eng-2017-0051.
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AbstractMethodology of analysis of stability is expounded to the one contour systems automatic control feedback in the presence of non-linearities. The methodology is based on the use of the simplest mathematical models of the nonlinear controllable systems. Stability of program manifolds of one contour automatic control systems is investigated. The sufficient conditions of program manifold’s absolute stability of one contour automatic control systems are obtained. The Hurwitz’s angle of absolute stability was determined. The sufficient conditions of program manifold’s absolute stability of control systems by the course of plane in the mode of autopilot are obtained by means Lyapunov’s second method.
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Кулик, Анатолий Степанович, Евгений Валерьевич Филиппович, Константин Юрьевич Дергачев, Сергей Николаевич Пасичник, and Юрий Александрович Немшилов. "УПРАВЛЕНЧЕСКИЕ МОДЕЛИ УГЛОВОГО ДВИЖЕНИЯ КОРОМЫСЛА С ВИНТОВЫМИ ЭЛЕКТРОПРИВОДАМИ." Aerospace technic and technology, no. 3 (June 26, 2020): 4–14. http://dx.doi.org/10.32620/aktt.2020.3.01.
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The subject of study in the article is the forming models' process for the angular motion of the rocker with screw electric actuators. The purpose is to develop the approach to the simplest models formation for the angular motion of the rocker with screw electric actuators as the automatic control object. Tasks: to form the physical model of rocker with screw electric actuators. Using the Lagrangian formalism develop the non-linear mathematical description of the angular motion process of a rocker with screw electric actuators. To obtain the linearized mathematical description of the automatic control object in form of state space in the cases when one sensor (angular position) and two sensors (angular position and angular velocity of the rocker) are used. To obtain the description of the automatic control object in the frequency domain using Laplace transforms. To form graphic models of the automatic control object using structural diagrams in the time and frequency domains. To analyze the functional properties of the automatic control object: stability, controllability, observability, structural and signal diagnosability in the cases when one sensor (angular position) and two sensors (angular position and angular velocity of the rocker) are used. To formulate the conditions for using mathematical descriptions as mathematical models of the automatic control object. The methods used are the Lagrange method, analytical linearization, state space, Laplace transform, Lypunov, Kalman criteria, diagnosability. The following results were obtained: the approach to the formation of the simplest models for the angular motion of a rocker with screw electric actuators as an object of automatic control for solving specific problems of analysis and synthesis was formed. Conclusions. The scientific novelty lies in the formation of the approach to the formation of the simplest control models for the angular motion of the rocker with screw electric actuators which differs from the known completeness of accounting for the acting forces and moments.
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Rongong, J. A., J. R. Wright, R. J. Wynne, and G. R. Tomlinson. "Modelling of a Hybrid Constrained Layer/Piezoceramic Approach to Active Damping." Journal of Vibration and Acoustics 119, no. 1 (January 1, 1997): 120–30. http://dx.doi.org/10.1115/1.2889679.
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It has been shown that significant reductions in structural vibration levels can be achieved using a hybrid system involving constrained layer damping and active control with piezoceramics. In this paper, mathematical models based on the Rayleigh Ritz approach, are developed to describe the longitudinal and flexural vibration behaviour of a cantilevered beam when excited using piezoceramic patches bonded to a constrained layer damping treatment. Predictions of static and steady state dynamic behaviour, obtained using the models are validated by comparison with results from finite element analysis and laboratory experiments. The models are then used in open loop and closed loop velocity feedback control simulations to demonstrate the improvements in stability and performance achieved using this method over that achieved using conventional active control.
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Akimov, Pavel A. "Correct Discrete-Continual Finite Element Method of Structural Analysis Based on Precise Analytical Solutions of Resulting Multipoint Boundary Problems for Systems of Ordinary Differential Equations." Applied Mechanics and Materials 204-208 (October 2012): 4502–5. http://dx.doi.org/10.4028/www.scientific.net/amm.204-208.4502.
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The distinctive paper is devoted to correct discrete-continual finite element method (DCFEM) of structural analysis based on precise analytical solutions of resulting multipoint boundary problems for systems of ordinary differential equations with piecewise-constant coefficients. Corresponding semianalytical (discrete-continual) formulations are contemporary mathematical models which currently becoming available for computer realization. Major peculiarities of DCFEM include uni-versality, computer-oriented algorithm involving theory of distributions, computational stability, optimal conditionality of resulting systems and partial Jordan decompositions of matrices of coeffi-cients, eliminating necessity of calculation of root vectors.
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Norkus, Arnoldas, and Romanas Karkauskas. "STEPPED OPTIMIZATION ALGORITHM FOR LIGHT‐WEIGHT ELASTIC‐PLASTIC STRUCTURES CONSIDERING LOAD COMBINATIONS." Technological and Economic Development of Economy 11, no. 4 (December 31, 2005): 302–9. http://dx.doi.org/10.3846/13928619.2005.9637712.
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The aim of the article is to present a developed algorithm of a stepped structural optimization method in the case of load combinations. The presentation of external loading via load combinations usually is employed in design codes. The pin‐jointed steel structures as light‐weight ones are widely used in actual engineering practice. The employment of dissipative features of material via elastic‐plastic model ensures a significant reduction of structural carrying capacity reserves (essential economic effect) versus the employment of structural response only in the elastic range. The stability, stiffness, constructional requirements and actual functions for cross‐sectional properties of standard profiles are employed in the optimization process aiming to obtain an optimal light‐weight structure which deformed behavior is compatible with codified requirements for such class of engineering structures. FEM mathematical models realizing structural optimization method steps are developed.
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Arnoldi, Jean-François, and Bart Haegeman. "Unifying dynamical and structural stability of equilibria." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2193 (September 2016): 20150874. http://dx.doi.org/10.1098/rspa.2015.0874.
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We exhibit a fundamental relationship between measures of dynamical and structural stability of linear dynamical systems—e.g. linearized models in the vicinity of equilibria. We show that dynamical stability, quantified via the response to external perturbations (i.e. perturbation of dynamical variables), coincides with the minimal internal perturbation (i.e. perturbations of interactions between variables) able to render the system unstable. First, by reformulating a result of control theory, we explain that harmonic external perturbations reflect the spectral sensitivity of the Jacobian matrix at the equilibrium, with respect to constant changes of its coefficients. However, for this equivalence to hold, imaginary changes of the Jacobian’s coefficients have to be allowed. The connection with dynamical stability is thus lost for real dynamical systems. We show that this issue can be avoided, thus recovering the fundamental link between dynamical and structural stability, by considering stochastic noise as external and internal perturbations. More precisely, we demonstrate that a linear system’s response to white-noise perturbations directly reflects the intensity of internal white-noise disturbance that it can accommodate before becoming stochastically unstable.
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Yazyev, Serdar, Yu Konoplev, Svetlana Yazyeva, and Leysan Akhtyamova. "Buckling of rotating rods under the action of axial compressive forces taking into account their own weight." Construction and Architecture 8, no. 3 (August 1, 2020): 12–22. http://dx.doi.org/10.29039/2308-0191-2020-8-3-12-22.
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The article is devoted to the conclusion of resolving equations for solving the tasks of bulging rotating rods subject to the action of compressive co-centric forces taking into account uniformly distributed load along the axis.
In this mode, for example, fast-moving shafts operate.
The purpose of this article is to provide an engineer with a method for calculating drill pipes, tested diagrams and justification of conditions in rotary drilling.
The new mathematical models describing stability of rods taking into account own weight and new software are proposed. Numerical simulation of load intensity distributions in the rod along the axis was carried out, at the same time different types of boundary conditions of rod fixation are used.
Mathematical models and software for numerical simulation of stability of rotating rods under action of axial compressive forces have been improved.
Note that the effect of torsion moment in the present case may not be considered as insignificant in comparison with the above loads.
A new method of calculating stability of rotating rods, allowing to take into account any boundary conditions and taking into account own weight, has been developed and scientifically justified.
There are proposed mathematical expressions convenient for practical use, which give very accurate results.
Obtained results can be used in evaluation and diagnostics of state of samples of structural materials, in process of experimental investigations and in investigation of fast-flowing rotating processes in rod structures of variable stiffness, made of anisotropic composite materials in machine-building, shipbuilding, aircraft engineering, instrument-making, power engineering, etc.
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Bascetta, Luca, Marcello Farina, Alessandro Gabrielli, and Matteo Matteucci. "A feedback linearisation algorithm for single-track models with structural stability properties." Control Engineering Practice 128 (November 2022): 105318. http://dx.doi.org/10.1016/j.conengprac.2022.105318.
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Harfash, A. J. "Structural stability for convection models in a reacting porous medium with magnetic field effect." Ricerche di Matematica 63, no. 1 (April 11, 2013): 1–13. http://dx.doi.org/10.1007/s11587-013-0152-x.
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Katanov, Yuriy, Yuriy Vaganov, and Matvey Cheymetov. "Neural simulation-based analysis of the well wall stability while productive seam penetrating." Mining of Mineral Deposits 15, no. 4 (December 2021): 91–98. http://dx.doi.org/10.33271/mining15.04.091.
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Purpose is the development of mathematical models to evaluate deformation of parameters of the rock mass-well geological and engineering system within the anisotropic media. Methods. Both mathematical and neural modeling of a stress state of the rock mass-well system under conditions of geological uncertainty has been applied for the studies. From the viewpoint of mathematical modeling, analysis of probability of factors, complicating drilling, should involve a number of assumptions for strength and deformation characteristics of rock mass layers corresponding to particular hole-making conditions. Findings. A mathematical model of horizontal wellbore and geological layers, occurring along the structure under the conditions of permanent comprehensive stresses, has been developed. An analytical and graphical form has been applied to implement one of the basic aspects of aggregation principles of strength changes in each particular lithological layer for identification of an ideal value of horizontal/inclined wellbore length relative to the rock mass depths scheduled by mining. Regularities of changes in deformation and spatial well stability within the complex reservoirs depending upon various process duties have been determined. A neural simulation-based model has been proposed to analyze deformation of rock mass layers having different strength characteristics. Originality. Interaction between geomechanical characteristics of rock mass as well as deformation and spatial stability of well design has been evaluated both qualitatively and quantitatively. Practical implications. An opportunity has been presented to forecast deformation of well walls taking into consideration different strength as well as structural and geological rock mass characteristics on the basis of neural simulation. The represented approach has been included on the register of the best scientific-based practices according to “Methods to recover low-pressure gas of Cenomanian producing complex” Project.
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Sobchuk, V., A. Laptev, I. Salandа, and Yu Sachuk. "MATHEMATICAL MODEL OF INFORMATION NETWORK STRUCTURE ON THE BASIS OF NON-STATIONARY HIERARCHICAL AND STATIONARY HYPERSLETS." Collection of scientific works of the Military Institute of Kyiv National Taras Shevchenko University, no. 64 (2019): 124–32. http://dx.doi.org/10.17721/2519-481x/2019/64-12.
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The article developed a model of the structure of an integrated information network based on a nonstationary hierarchical and stationary hypernetwork, taking into account the destructive effects of various kinds. The functional stability of the integrated information network in the work is understood as the ability of the system to function, albeit with a decrease in quality, for a given time under the influence of external and internal destabilizing factors. External and internal destabilizing factors are understood as failures, malfunctions of system elements, deliberate damages, combat defeats, electromagnetic interferences, maintenance personnel errors. Ensuring the functional stability of any complex technical system is carried out in three stages: identifying abnormal situations, localizing abnormal situations, restoring operation due to the redistribution of resources. When considering integrated information networks from the point of view of functional stability, the failure of a switching node or communication line entails the destruction of the transmission channels of secondary networks, in the graphs of these networks are non-adjacent. Therefore, it is impractical to model the structure of such a network by a graph. In this regard, introduced new concepts and definitions in the theory of functional stability and developed an appropriate methodological apparatus. This model takes into account all the necessary basic parameters from the point of view of functional stability of the network, their properties and relations, which have a significant impact on the synthesis of the optimal network structure. The difference between a hypernetwork and other structural models is that the creation of a hypernetwork structure involves more than two generating sets, allows you to take into account the influence of possible emergency situations caused by internal and external factors.
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Kou, Farong, Qiangqiang Jing, Chen Chen, and Jianghao Wu. "Endocrine Composite Skyhook-Groundhook Control of Electromagnetic Linear Hybrid Active Suspension." Shock and Vibration 2020 (February 29, 2020): 1–17. http://dx.doi.org/10.1155/2020/3402168.
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In order to effectively improve vehicle riding comfort, handling stability, and realize vibration energy recovery, a new kind of electromagnetic linear hybrid active suspension (EMLHAS) integrated with linear motor and solenoid valve shock absorber is put forward. Firstly, for the analysis of the suspension performance, a quarter dynamic model of EMLHAS is established. At the same time, the mathematical models of a linear motor, including the active state and energy-regenerative state, are found. The correctness of mathematical models for the linear motor in the active and energy-regenerative states is verified by means of characteristic tests. Moreover, the velocity characteristic tests of solenoid valve shock absorber are carried out to determine its mathematical polynomial model in the semiactive state. Then, a new kind of multimode endocrine composite skyhook-groundhook control strategy is proposed. The suspension motion is divided into four modes according to the driving conditions of the vehicle. An endocrine control with long feedback and short feedback is combined with the skyhook-groundhook control. The control laws of the skyhook-groundhook controller and endocrine controller are, respectively, designed. Finally, the simulation analysis of suspension dynamic performance and energy-regenerative characteristic is done. The results show the control effect of endocrine composite skyhook-groundhook control is better than that of skyhook-groundhook control, which improves vehicle riding comfort and handling stability. Moreover, part of vibration energy is recovered.
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Wang, D. Q., C. J. Wu, and R. C. Yang. "An Insight into the Analytical Models of Granular Particle Damping." Advanced Materials Research 819 (September 2013): 13–19. http://dx.doi.org/10.4028/www.scientific.net/amr.819.13.
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Granular particle damping technique is a means for achieving high structural damping by the use of metal particles filled into an enclosure which is attached to the structure in a region of high vibration levels. The particle dampers are now preferred over traditional dampers due to the stability, robustness, cost effectiveness and the lower noise level than the impact damper. Such a promising technique has been used successfully in many fields over the past 20 years. In this paper, a state-of-art review on the development of modeling for particle damping is presented. The fundamentals and individual features of three main mathematical models of the granular particle damping are briefly summarized, i.e. the lumped mass model, the Discrete Element Method (DEM) and the approach based on the multiphase flow (MPF) theory of gas-particle. It is worth noting that an improved analytical model of the particle damping based on MPF theory is also introduced. The co-simulation of the COMSOL Multiphysics live link for MATLAB is conducted using this improved model. It can be shown that this model makes the complicated modeling problem more simply and offers the possibility to analyze the more complex particle-damping vibrating system.
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Potachits, Ya V. "A Study of the Occurrence of Resonance under the Influence of Dynamic Forces on the Structural Elements of Electrical Installations." ENERGETIKA. Proceedings of CIS higher education institutions and power engineering associations 64, no. 3 (June 4, 2021): 228–38. http://dx.doi.org/10.21122/1029-7448-2021-64-3-228-238.
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The increase in the levels of short-circuit currents in the power system of the Republic of Belarus requires the study of the parameters of the electrodynamic stability of the main structural elements of electrical installations with flexible conductors. In case of a short circuit in the network, currents tenfold exceeding the rated one hundreds of times can flow through the current-carrying part of the device. When the magnetic fields formed by these currents interact, significant electromagnetic forces arise, which have a destructive effect both on the current-carrying parts themselves and on the structural elements of electrical installations, viz. support insulators, switching devices, measuring equipment. The movement of the wires in a short-circuit mode leads to the appearance of significant dynamic loads in them, which, in turn, are transmitted to the portals, support insulators and electrical devices. A topical problem is the occurrence of unacceptable mechanical forces in the main structural elements that can cause their destruction. Thus, the analysis of the physical and mechanical parameters and geometric dimensions of the flexible busbar of switchgear shows that a violation of the condition of electrodynamic resistance to tension is unlikely due to the high mechanical strength of the large-section steel-aluminum wires used. At the same time, span-limiting portals, support insulators and other electrical devices have significantly lower permissible bending loads. When exposed to dynamic forces, the conductors bend and transfer the load to the structural elements which have certain elasticity. Thus, a reliable determination of dynamic loads, taking into account the current-carrying parts acting on the supporting structures, is possible only if a dynamic task is set. The article describes the methods of mathematical modeling and computational experiment for analyzing the parameters of the electro-dynamic stability of the main structural elements which are determined using coefficients that depend on the natural frequencies of oscillations and the nature of changes in dynamic forces over time. To solve these problems, mathematical models are compiled and boundary value problems are formulated for calculating the electrodynamic stability of structural elements, taking into account the possible coincidence of the frequencies of natural and forced oscillations of structural elements taking into account the probable coincidence of the frequencies of forced and natural vibrations of structural elements.
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COOMBES, S., Y. M. LAI, M. ŞAYLI, and R. THUL. "Networks of piecewise linear neural mass models." European Journal of Applied Mathematics 29, no. 5 (February 20, 2018): 869–90. http://dx.doi.org/10.1017/s0956792518000050.
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Neural mass models are ubiquitous in large-scale brain modelling. At the node level, they are written in terms of a set of ordinary differential equations with a non-linearity that is typically a sigmoidal shape. Using structural data from brain atlases, they may be connected into a network to investigate the emergence of functional dynamic states, such as synchrony. With the simple restriction of the classic sigmoidal non-linearity to a piecewise linear caricature, we show that the famous Wilson–Cowan neural mass model can be explicitly analysed at both the node and network level. The construction of periodic orbits at the node level is achieved by patching together matrix exponential solutions, and stability is determined using Floquet theory. For networks with interactions described by circulant matrices, we show that the stability of the synchronous state can be determined in terms of a low-dimensional Floquet problem parameterised by the eigenvalues of the interaction matrix. Moreover, this network Floquet problem is readily solved using linear algebra to predict the onset of spatio-temporal network patterns arising from a synchronous instability. We further consider the case of a discontinuous choice for the node non-linearity, namely the replacement of the sigmoid by a Heaviside non-linearity. This gives rise to a continuous-time switching network. At the node level, this allows for the existence of unstable sliding periodic orbits, which we explicitly construct. The stability of a periodic orbit is now treated with a modification of Floquet theory to treat the evolution of small perturbations through switching manifolds via the use of saltation matrices. At the network level, the stability analysis of the synchronous state is considerably more challenging. Here, we report on the use of ideas originally developed for the study of Glass networks to treat the stability of periodic network states in neural mass models with discontinuous interactions.
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Tkachuk, Mykola А., Andrey Grabovskiy, Mykola M. Tkachuk, Illia Klochkov, Mykola Prokopenko, Vladeslav Tretyak, and Iryna Voloshina. "THEORETICAL BASIS FOR ADVANCED SOLUTIONS OF HIGH RPM ELEMENTS OF CIVIL AND MILITARY MACHINES BASED ON STRENGTH AND DYNAMIC STABILITY CRITERIA." Bulletin of the National Technical University «KhPI» Series: Engineering and CAD, no. 1 (December 28, 2022): 79–84. http://dx.doi.org/10.20998/2079-0775.2022.1.08.
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In modern conditions, one of the significant obstacles to ensuring increased power, efficiency and resource of military and civilian vehicles is the exhausted possibilities of traditional technical solutions of basic elements and systems. This primarily applies to high-speed elements, in particular, turbines and rotary parts of air blowers of internal combustion engines, transmissions, drives, hydraulic machines and more. High speeds cause dynamic processes that can potentially lead to problems with strength, rigidity and stability. In order to substantiate the progressive technical solutions of high-speed parts, it is necessary to develop appropriate theoretical foundations for the analysis of processes that occur in these elements. The stress-strain state of the elements of rotor systems is of particular interest. It is also important to determine the stiffness properties of the elastic supports. In turn, this affects the stability of the rotor systems. This creates a basis for establishing patterns of influence of variable parameters on the characteristics of dynamic processes and states. A complex mathematical and numerical models of the stress-strain state and stability of motion of high-speed structural elements is developed on a unified methodological basis. These models are described by a common set of varied parameters. General criteria and restrictions are formulated. The search for advanced solutions is carried out by meeting certain complex criteria and constraints. Design parameters and operational modes are varied. The analysis problems are solved using a unified parametric model. Keywords: civil and military machines, RPM structural parts, stress-strain state, critical rotational velocity
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Tertyshna, Olena, Konstantin Zamikula, Oleg Tertyshny, Olena Zinchenko, and Petro Topilnytskyi. "Phase Equilibrium of Petroleum Dispersion Systems in Terms of Thermodynamics and Kinetics." Chemistry & Chemical Technology 15, no. 1 (February 15, 2021): 132–41. http://dx.doi.org/10.23939/chcht15.01.132.
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The process of paraffin formation has been considered, including the peculiarities of the paraffin structure as a result of phase transitions with a decreasing temperature. Mathematical models for thermodynamic and kinetic calculations of the "solid-liquid" system phase equilibrium have been developed. To shift the "fuel oil-paraffin" balance towards the liquid, it is necessary to reduce the activity ratio of solid and liquid phases by introducing into the system a substance with a lower solubility parameter. To increase the stability, as well as structural and mechanical characteristics of fuel oil, the additive of plant origin was synthesized. The phase transitions in fuel oil depending on the temperature when adding different amounts of additives have been studied.
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Elchahal, Ghassan, Pascal Lafon, and Rafic Younes. "Design optimization of floating breakwaters with an interdisciplinary fluid–solid structural problem." Canadian Journal of Civil Engineering 36, no. 11 (November 2009): 1732–43. http://dx.doi.org/10.1139/l09-095.
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The design optimization of floating breakwaters implicates solving an interdisciplinary problem consisting of three models. The first one arises from the interaction of linear waves with a moored floating breakwater with a leeward boundary that is composed of a vertical sidewall representing the quay wall in ports. The second covers the dynamical behaviour of the oscillating structure caused by the incoming waves. These two assemble the hydrodynamic performance of the floating breakwater; while the third concerns its structural mechanics subject to hydrostatic and hydrodynamic forces. The goal of the optimization problem is to design an optimal floating breakwater that can attenuate the waves to the minimum height inside the port and fulfill several constraints related to floating, stability, and structural resistance. The objective function and constraints are expressed in terms of geometrical parameters of the breakwater as mathematical expressions assembled in an optimization algorithm based on the sequential quadratic programming method (SQP). This yields to several optimal structures each corresponding to a specified wave period. Finally, an analysis is performed to determine an optimum structure for a wide range of frequencies.
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Berci, Marco. "On Aerodynamic Models for Flutter Analysis: A Systematic Overview and Comparative Assessment." Applied Mechanics 2, no. 3 (July 29, 2021): 516–41. http://dx.doi.org/10.3390/applmech2030029.
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This work reviews different analytical formulations for the time-dependent aerodynamic load of a thin aerofoil and clarifies numerical flutter results available in the literature for the typical section of a flexible wing; inviscid, two-dimensional, incompressible, potential flow is considered in all test cases. The latter are investigated using the exact theory for small airflow perturbations, which involves both circulatory and non-circulatory effects of different nature, complemented by the p-k flutter analysis. Starting from unsteady aerodynamics and ending with steady aerodynamics, quasi-unsteady and quasi-steady aerodynamic models are systematically derived by successive simplifications within a unified approach. The influence of the aerodynamic approximations on the aeroelastic stability boundary is then rigorously assessed from both physical and mathematical perspectives. All aerodynamic models are critically discussed and compared in the light of the numerical results as well, within a comprehensive theoretical framework in practice. In all cases, results accuracy depends on the aero-structural arrangement of the flexible wing; however, simplified unsteady and simplified quasi-unsteady aerodynamic approximations are suggested for robust flutter analysis whenever the wing’s elastic axis lies ahead of the aerofoil’s control point.
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Sivilevičius, Henrikas. "INFLUENCE OF HOMOGENEITY OF MINERAL MATERIALS' GRADING AND DOSING ERRORS ON THE STABILITY OF ASPHALT CONCRETE MIXTURE COMPOSITION." JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT 9, no. 1 (March 31, 2003): 25–35. http://dx.doi.org/10.3846/13923730.2003.10531298.
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Errors of optimal composition asphalt concrete mixture designed in the laboratory and their importance for road construction are investigated. After the analysis of asphalt concrete production according to the traditional technology, factors influencing its structure, characteristics and quality are systematised. Mathematical models of dependence of medium quadratic deviations of siftings of finite dosed mineral materials through control sieves on the means of siftings are estimated by a regressive analysis. Variations of grading of hot fractions 0–5 mm and 5–15 mm as well as cold mineral powder sieved through technological sieves of mixing equipment and influence of errors of dosing these mineral materials in the produced mixture on the stability of quantity of containing mineral components (crushed stone, sand and mineral filler) are identified. The main trends of asphalt concrete structure and handling of its equipment methods improvement are presented.
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BALDWIN, JOHN T. "COMPLETENESS AND CATEGORICITY (IN POWER): FORMALIZATION WITHOUT FOUNDATIONALISM." Bulletin of Symbolic Logic 20, no. 1 (March 2014): 39–79. http://dx.doi.org/10.1017/bsl.2014.3.
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AbstractWe propose a criterion to regard a property of a theory (in first or second order logic) as virtuous: the property must have significant mathematical consequences for the theory (or its models). We then rehearse results of Ajtai, Marek, Magidor, H. Friedman and Solovay to argue that for second order logic, ‘categoricity’ has little virtue. For first order logic, categoricity is trivial; but ‘categoricity in power’ has enormous structural consequences for any of the theories satisfying it. The stability hierarchy extends this virtue to other complete theories. The interaction of model theory and traditional mathematics is examined by considering the views of such as Bourbaki, Hrushovski, Kazhdan, and Shelah to flesh out the argument that the main impact of formal methods on mathematics is using formal definability to obtain results in ‘mainstream’ mathematics. Moreover, these methods (e.g., the stability hierarchy) provide an organization for much mathematics which gives specific content to dreams of Bourbaki about the architecture of mathematics.
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Song, Xinke, Demin Chen, and Baohua Qu. "Topology optimization of robotic arm for gas drainage pipeline installation." Journal of Physics: Conference Series 2383, no. 1 (December 1, 2022): 012014. http://dx.doi.org/10.1088/1742-6596/2383/1/012014.
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By means of finite element analysis and topology optimization methods, the structural optimization and lightweight design of the robotic arm for the installation of gas drainage pipelines are realized, so that it can realize more complex actions under the premise of ensuring stability. SolidWorks 3D modeling and Ansys Workbench analysis software are used to build models of the robotic arm and perform static analysis. The structural design is optimized through the deformation and stress distribution when grasping the maximum weight. The topology optimization mathematical model of the variable density method and the SIMP (Simplified Isotropic Material with Penalization) interpolation model was constructed, and the topology optimization of the robotic arm was performed in the Shape Optimization module in Ansys Workbench. On this basis, the structure after topology optimization is analyzed and studied. The results show that compared with before topology optimization, the mass of the manipulator is reduced by 29.65%, and the maximum deformation and maximum stress are both reduced by 10%, which confirms the feasibility of lightweight design and structural optimization of the manipulator.
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Minami, Nathan A. "Using Phenomenological Research to Drive Dynamic Modeling." International Journal of Agent Technologies and Systems 4, no. 2 (April 2012): 60–77. http://dx.doi.org/10.4018/jats.2012040104.
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One of the most difficult aspects in mathematical modeling and simulation is developing data to drive models and learning. This is particularly difficult when the subject involves intangible variables and concepts such as stress and perceptions that are difficult to ascribe a quantitative value to. This paper provides a description of how qualitative data collected during in depth phenomenological interviews with subject matter experts can be used to drive models. It also provides a case study of insurgency warfare and coalition and Afghan National Government performance during the last ten years. The U.S. government has spent more than $300 billion on the war in Afghanistan. Despite the employment of these resources, the goal of creating stability in the country has not been achieved. Twenty U.S. Army officers with six or more months of experience in Afghanistan were selected by random choice from a specific group. The participants were then interviewed to determine the meaning of their experiences in fighting an insurgency. Data analysis included organizing responses by question to identify the frequency of trends, patterns, and themes; and development of textural and structural descriptions of resource allocation and stability within the context of this study. Data was then transformed to create look-up tables that can be used to model, calibrate, and ascribe quantitative values to various variables in a dynamic insurgency model. A proof of concept model was then created to demonstrate the potential utility and power behind a model that combines the qualities of quantitative mathematical science and qualitative research methodology.
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Avalos, George, and Pelin G. Geredeli. "Stability analysis of coupled structural acoustics PDE models under thermal effects and with no additional dissipation." Mathematische Nachrichten 292, no. 5 (November 27, 2018): 939–60. http://dx.doi.org/10.1002/mana.201700489.
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Toroptsev, E. L., A. S. Marakhovskii, and R. R. Duszynski. "Intersectoral modeling of transients." Economic Analysis: Theory and Practice 19, no. 3 (March 30, 2020): 564–85. http://dx.doi.org/10.24891/ea.19.3.564.
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Subject. The article considers structural transition processes in macroeconomics. Objectives. The aim is to present our own concept and mathematical tools to study structural transitions in macroeconomics. Dynamic inter-industry balance enables to formalize the problem in the form of a Koshi task for ordinary differential equations. Methods. The methodology components include the basics of inter-industry and numerical analysis and modeling of linear or linearized dynamic systems, integral criteria of system dynamics, stability and quality of transitional processes. We also apply a technique for analyzing the own dynamic properties of economic systems that solve the same sustainability-related challenges, but on the basis of algebraic methods and criteria. Results. We offer methods and mathematical tools for numerical study of sustainability and structural dynamics of macroeconomics. These methods are focused on integrating high-dimensional balance models and integral criteria for the quality of transition periods in the economy. The paper unveils advantages of calculating the matrix exponential and its integral in tasks involving analysis and forecasting, over other numerical methods. The proposed method permits to effectively build a difference scheme to integrate with any step of observation of the solution. In this case, the work step of integration is generated in the algorithm automatically, depending on changes in gross output. Conclusions. The paper presents a unique option to analyze transitional processes in macroeconomics. It is designed to develop and evaluate the results of pursued economic policy.
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A.V., Chistyakov. "On improving the efficiency of mathematical modeling of the problem of stability of construction." Artificial Intelligence 25, no. 3 (October 10, 2020): 27–36. http://dx.doi.org/10.15407/jai2020.03.027.
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Algorithmic software for mathematical modeling of structural stability is considered, which is reduced to solving a partial generalized eigenvalues problem of sparse matrices, with automatic parallelization of calculations on modern parallel computers with graphics processors. Peculiarities of realization of parallel algorithms for different structures of sparse matrices are presented. The times of solving the problem of stability of composite materialsusing a three-dimensional model of "finite size fibers" on computers of different architectures are given. In mathematical modeling of physical and technical processes in many cases there is a need to solve problems of algebraic problem of eigenvalues (APVZ) with sparse matrices of large volumes. In particular, such problems arise in the analysis of the strength of structures in civil and industrial construction, aircraft construction, electric welding, etc. The solving to these problems is to determine the eigenvalues and eigenvectors of sparse matrices of different structure. The efficiency of solving these problems largely depends on the effectiveness of mathematical modeling of the problem as a whole. Continuous growth of task parameters, calculation of more complete models of objects and processes on computers require an increase in computer productivity. High-performance computing requirements are far ahead of traditional parallel computing, even with multicore processors. High-performance computing requirements are far ahead of traditional parallel computing, even with multicore processors. Today, this problem is solved by using powerful supercomputers of hybrid architecture, such as computers with multicore processors (CPUs) and graphics processors (GPUs), which combine MIMD and SIMD architectures. But the potential of high-performance computers can be used to the fullest only with algorithmic software that takes into account both the properties of the task and the features of the hybrid architecture. Complicating the architecture of modern high-performance supercomputers of hybrid architecture, which are actively used for mathematical modeling (increasing the number of computer processors and cores, different types of computer memory, different programming technologies, etc.) means a significant complication of efficient use of these resources in creating parallel algorithms and programs. here are problems with the creation of algorithmic software with automatic execution of stages of work, which are associated with the efficient use of computing resources, ways to store and process sparse matrices, analysis of the reliability of computer results. This makes it possible to significantly increase the efficiency of mathematical modeling of practical problems on modern high-performance computers, as well as free users from the problems of parallelization of complex problems. he developed algorithmic software automatically implements all stages of parallel computing and processing of sparse matrices on a hybrid computer. It was used at the Institute of Mechanics named after S.P. Tymoshenko NAS of Ukraine in modeling the strength problems of composite material. A significant improvement in the time characteristics of mathematical modeling was obtained. Problems of mathematical modeling of the properties of composite materials has an important role in designing the processes of deformation and destruction of products in various subject areas. Algorithmic software for mathematical modeling of structural stability is considered, which is reduced to solving a partial generalized problem of eigen values of sparse matrices of different structure of large orders, with automatic parallelization of calculations on modern parallel computers with graphics processors. The main methodological principles and features of implementation of parallel algorithms for different structures of sparse matrices are presented, which ensure effective implementation of multilevel parallelism of a hybrid system and reduce data exchange time during the computational process. As an example of these approaches, a hybrid algorithm of the iteration method in subspace for tape and block-diagonal matrices with a frame for computers of hybrid architecture is given. Peculiarities of data decomposition for matrices of profile structure at realization of parallel algorithms are considered. The proposed approach provides automatic determination of the required topology of the hybrid computer and the optimal amount of resources for the organization of an efficient computational process. The results of testing the developed algorithmic software for problems from the collection of the University of Florida, as well as the times of solving the problem of stability of composite materials using a three-dimensional model of "finite size fibers" on computers of different architectures. The results show a significant improvement in the time characteristics of solving problems.
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Yong, Wen-An, and Yizhou Zhou. "Recent Advances on Boundary Conditions for Equations in Nonequilibrium Thermodynamics." Symmetry 13, no. 9 (September 16, 2021): 1710. http://dx.doi.org/10.3390/sym13091710.
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This paper is concerned with modeling nonequilibrium phenomena in spatial domains with boundaries. The resultant models consist of hyperbolic systems of first-order partial differential equations with boundary conditions (BCs). Taking a linearized moment closure system as an example, we show that the structural stability condition and the uniform Kreiss condition do not automatically guarantee the compatibility of the models with the corresponding classical models. This motivated the generalized Kreiss condition (GKC)—a strengthened version of the uniform Kreiss condition. Under the GKC and the structural stability condition, we show how to derive the reduced BCs for the equilibrium systems as the classical models. For linearized problems, the validity of the reduced BCs can be rigorously verified. Furthermore, we use a simple example to show how thus far developed theory can be used to construct proper BCs for equations modeling nonequilibrium phenomena in spatial domains with boundaries.
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Easa, Said M., and Essam Dabbour. "Design radius requirements for simple horizontal curves on three-dimensional alignments." Canadian Journal of Civil Engineering 30, no. 6 (December 1, 2003): 1022–33. http://dx.doi.org/10.1139/l03-022.
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Current North American design guides have established mathematical relationships to calculate the minimum radius required for horizontal curves as a function of design speed, maximum superelevation, and maximum side friction. For three-dimensional (3-D) alignments, the design guides consider the alignment as two separate horizontal and vertical alignments and consequently ignore the effect of vertical alignment. This paper evaluates the effect of vertical alignment on minimum radius requirements using computer simulation, with a focus on trucks. For 3-D alignments, the results showed that existing design guidelines for minimum radius need to be increased by as much as 20% to achieve the same comfort limit on flat horizontal curves. It is interesting to note that in some cases truck rollover occurred before the side-friction comfort level is reached. This indicates the need for developing a different design control for trucks on 3-D alignments than the comfort criterion used for passenger cars on flat horizontal curves. Based on the simulation results, mathematical models for design radius requirements for passenger cars and trucks were developed.Key words: geometric design, horizontal curve radius, three-dimensional alignments, vehicle stability.
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Chen, Cheng-Wu. "Modeling and Fuzzy PDC Control and Its Application to an Oscillatory TLP Structure." Mathematical Problems in Engineering 2010 (2010): 1–13. http://dx.doi.org/10.1155/2010/120403.
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An analytical solution is derived to describe the wave-induced flow field and surge motion of a deformable platform structure controlled with fuzzy controllers in an oceanic environment. In the controller design procedure, a parallel distributed compensation (PDC) scheme is utilized to construct a global fuzzy logic controller by blending all local state feedback controllers. The Lyapunov method is used to carry out stability analysis of a real system structure. The corresponding boundary value problems are then incorporated into scattering and radiation problems. These are analytically solved, based on the separation of variables, to obtain a series of solutions showing the harmonic incident wave motion and surge motion. The dependence of the wave-induced flow field and its resonant frequency on wave characteristics and structural properties including platform width, thickness and mass can thus be drawn with a parametric approach. The wave-induced displacement of the surge motion is determined from these mathematical models. The vibration of the floating structure and mechanical motion caused by the wave force are also discussed analytically based on fuzzy logic theory and the mathematical framework to find the decay in amplitude of the surge motion in the tension leg platform (TLP) system. The expected effects of the damping in amplitude of the surge motion due to the control force on the structural response are obvious.